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arXiv · 1711.05169

On the Complex Cayley Grassmannian

Üstün Yıldırım
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Abstract

We define a torus action on the (complex) Cayley Grassmannian $X$. Using this action, we prove that $X$ is a singular variety. We also show that the singular locus is smooth and has the same cohomology ring as that of $\mathbb{CP}^5$. Furthermore, we identify the singular locus with a quotient of $G_2^\mathbb{C}$ by a parabolic subgroup.

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Üstün Yıldırım. 2019-02-27. On the Complex Cayley Grassmannian. https://arxiv.org/abs/1711.05169

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